Demonstrates the consolidation of important areas, such as algebraic statistics, computational commutative algebra, and deeper aspects of graphical models. It includes, among many others, new results and applications in cubic regression models for mixture experiments, multidimensional Fourier regression experiments, topological methods for multivariate statistics, Fourier analysis over the dihedral groups, new results related to discrete-time semi Markov processes, and the Hewitt-Savage zero-one law.